Established in scope
Clock-compatible marking fibre and canonical polar distance
In the question: Historical: common source, state and event selection
Completeness only for the stated operator-compatibility class. Countermarks are not full P1 sources and need not obey the original polar rule. Unique distance minimization does not prove a physical law minimizing that distance or matrix positivity from reflection positivity.
Read the exact result, assumptions and evidence
Result
The entire stated native mark class is P=F-cc*, [c] in CP1(E+), or RP1 for real projectors. Every point gives the same quarter spectrum and square; q families are natively S3fix-equivariant. The native q/sigma stabilizer cannot remove the parameter. Original cpol=-sqrt(3/5)e0+sqrt(2/5)e1 and c=e0 differ exactly: HS squared4/5, marked-ray responses2/5 versus0. Uq is also the uniquely nearest isometry to actual orthonormalized Dq, with Frobenius cost7-2sqrt6.
Required assumptions
- Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
- Original clock/simplex without an imposed polar mark
Retain actual normalized W6 simplex, sigma=(234), tau=(01), q=5. Consider ALL Hermitian rank2 projectors P with RanP inside Fixsigma, [P,tau]=0 and one positive/one negative tau eigenvalue on RanP. The original polar rule is a comparison point, not an imposed condition of this compatibility class.
Original evidence
- SOURCE-SELECTION.md lines 28–111
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/SOURCE-SELECTION.md
ab3bbe0344406a83bf66e22664183a60281fb744fc5057c394624c74ba6e8256
finding:native-clock-compatible-polar-fibre-and-canonical-distance